Elliptic curve data - 73920.gk2

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• ec_curvedata •

  Column	Type
  Ciso	text
  Clabel	text
  Cnumber	smallint
  abc_quality	double precision
  absD	numeric
  adelic_genus	integer
  adelic_index	integer
  adelic_level	bigint
  ainvs	numeric[]
  analytic_rank	smallint
  bad_primes	integer[]
  class_deg	smallint
  class_size	smallint
  cm	smallint
  conductor	integer
  degree	bigint
  elladic_images	text[]
  faltings_height	numeric
  faltings_index	smallint
  faltings_ratio	smallint
  iso_nlabel	smallint
  isogeny_degrees	smallint[]
  jinv	numeric[]
  lmfdb_iso	text
  lmfdb_label	text
  lmfdb_number	smallint
  manin_constant	smallint
  min_quad_twist_ainvs	numeric[]
  min_quad_twist_disc	smallint
  modell_images	text[]
  modm_images	text[]
  nonmax_primes	smallint[]
  nonmax_rad	integer
  num_bad_primes	smallint
  num_int_pts	integer
  optimality	smallint
  potential_good_reduction	boolean
  rank	smallint
  regulator	numeric
  semistable	boolean
  sha	integer
  sha_primes	smallint[]
  signD	smallint
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '73920df', 'Clabel': '73920df2', 'Cnumber': 2, 'abc_quality': 1.1359981314962933, 'absD': 368437864693414389350400, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 840, 'ainvs': [0, 1, 0, -17941665, -1667779137], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 7, 11], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 73920, 'degree': 9633792, 'elladic_images': ['4.12.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.2115033757868118491743451841', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 166, 'isogeny_degrees': [1, 2], 'jinv': [2436531580079063806249, 1405478914998681600], 'lmfdb_iso': '73920.gk', 'lmfdb_label': '73920.gk2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 0, -280338, -3362508], 'min_quad_twist_disc': 8, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '4.12.0-2.a.1.1', '24.24.0-24.a.1.4', '280.24.0.?', '420.24.0.?', '840.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 9, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '3.3705205064998489757219383076', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '2.1717826049468938850484970019', 'prec': 100}, 'szpiro_ratio': 5.505570450290481, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [2, 2]}
• ec_classdata •

  Column	Type
  anlist	smallint[]
  aplist	smallint[]
  class_deg	smallint
  class_size	smallint
  conductor	integer
  isogeny_matrix	smallint[]
  lmfdb_iso	text
  trace_hash	bigint

  
  {'anlist': [0, 1, 0, 1, 0, 1, 0, -1, 0, 1, 0, -1, 0, -6, 0, 1, 0, 2, 0, 0, 0], 'aplist': [0, 1, 1, -1, -1, -6, 2, 0, 0, 6, -8, -10, -2, 8, 4, 6, 12, -10, -8, 4, 10, 8, -12, 6, 2], 'class_deg': 4, 'class_size': 4, 'conductor': 73920, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '73920.gk', 'trace_hash': 809007875209756923}
• ec_mwbsd •

  Column	Type
  area	numeric
  conductor	integer
  gens	numeric[]
  heights	numeric[]
  lmfdb_label	text
  ngens	smallint
  rank_bounds	smallint[]
  real_period	numeric
  sha_an	numeric
  special_value	numeric
  tamagawa_product	integer
  torsion_generators	numeric[]
  xcoord_integral_points	numeric[]

  
  {'area': {'__RealLiteral__': 0, 'data': '0.0016237666246965895555220033904', 'prec': 110}, 'conductor': 73920, 'gens': [[-579, 92340, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '3.3705205064998489757219383076', 'prec': 100}], 'lmfdb_label': '73920.gk2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.079989712697069177820606387179', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '7.5489950747260841653354183373759523462', 'prec': 130}, 'tamagawa_product': 448, 'torsion_generators': [[-93, 0, 1], [4281, 0, 1]], 'xcoord_integral_points': [-4189, -3342, -579, -93, 4281, 36771]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [2, 0], '5': [4, 0], '7': [1, 0], '11': [1, 0], '13': [1, 0], '17': [1, 0], '19': [1, 1, 0], '23': [1, 1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '73920.gk2'}
• ec_torsion_growth •

  Column	Type
  degree	smallint
  field	numeric[]
  lmfdb_label	text
  torsion	smallint[]

  
  
  • id: 3497778
    {'degree': 2, 'field': [6, 0, 1], 'lmfdb_label': '73920.gk2', 'torsion': [2, 4]}
  • id: 3497780
    {'degree': 4, 'field': [256, 0, -38, 0, 1], 'lmfdb_label': '73920.gk2', 'torsion': [2, 4]}
  • id: 3497779
    {'degree': 4, 'field': [1225, 0, 0, 0, 1], 'lmfdb_label': '73920.gk2', 'torsion': [2, 4]}
  • id: 3497783
    {'degree': 8, 'field': [-196608, 0, 102752, 0, -1536, 0, 0, 0, 1], 'lmfdb_label': '73920.gk2', 'torsion': [2, 6]}
  • id: 3497782
    {'degree': 8, 'field': [256, 0, -256, 0, 120, 0, -16, 0, 1], 'lmfdb_label': '73920.gk2', 'torsion': [2, 8]}
  • id: 3497781
    {'degree': 8, 'field': [4096, 0, 0, 0, 233, 0, 0, 0, 1], 'lmfdb_label': '73920.gk2', 'torsion': [4, 4]}
  • id: 3497785
    {'degree': 16, 'field': [-14594208856380, 100943947792080, -36150877589940, 2630267614080, 196980085881, -107533933308, 30685038144, -2846302668, -41072828, 43090488, -7128196, 149076, 51144, -36, -388, 0, 1], 'lmfdb_label': '73920.gk2', 'torsion': [2, 8]}
  • id: 3497786
    {'degree': 16, 'field': [1731260476, -924274696, 834656420, 149126348, 1428030, -93219640, 34538149, -3140504, 1016604, -183410, 66965, -18052, 4313, -630, 110, -8, 1], 'lmfdb_label': '73920.gk2', 'torsion': [2, 12]}
  • id: 3497784
    {'degree': 16, 'field': [7745936121, 0, -62868960, 0, 894048736, 0, 182397320, 0, 9945366, 0, 78880, 0, -4944, 0, -40, 0, 1], 'lmfdb_label': '73920.gk2', 'torsion': [2, 8]}
• ec_localdata •

  Column	Type
  conductor	integer
  conductor_valuation	smallint
  discriminant_valuation	smallint
  j_denominator_valuation	smallint
  kodaira_symbol	smallint
  lmfdb_label	text
  prime	integer
  reduction_type	smallint
  root_number	smallint
  tamagawa_number	smallint

  
  
  • id: 1793505
    {'conductor': 73920, 'conductor_valuation': 6, 'discriminant_valuation': 32, 'j_denominator_valuation': 14, 'kodaira_symbol': -26, 'lmfdb_label': '73920.gk2', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 1793506
    {'conductor': 73920, 'conductor_valuation': 1, 'discriminant_valuation': 14, 'j_denominator_valuation': 14, 'kodaira_symbol': 18, 'lmfdb_label': '73920.gk2', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 14}
  • id: 1793507
    {'conductor': 73920, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '73920.gk2', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 1793508
    {'conductor': 73920, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '73920.gk2', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 1793509
    {'conductor': 73920, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '73920.gk2', 'prime': 11, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
• ec_galrep •

  Column	Type
  adelic_gens	bigint[]
  adelic_image	text
  conductor	integer
  elladic_image	text
  lmfdb_label	text
  modell_image	text
  prime	smallint

  
  
  • id: 2152522
    {'adelic_gens': [[837, 4, 836, 5], [419, 836, 838, 831], [213, 4, 422, 3], [1, 4, 0, 1], [281, 2, 0, 1], [171, 2, 166, 839], [1, 0, 4, 1], [723, 2, 358, 839]], 'adelic_image': '840.48.0.?', 'conductor': 73920, 'lmfdb_label': '73920.gk2', 'prime': 0}
  • id: 306140
    {'conductor': 73920, 'elladic_image': '4.12.0.1', 'lmfdb_label': '73920.gk2', 'modell_image': '2Cs', 'prime': 2}
• ec_padic •

  Column	Type
  lmfdb_iso	text
  p	smallint
  prec	smallint
  unit	numeric
  val	smallint

  
  
  • id: 3797268
    {'lmfdb_iso': '73920.gk', 'p': 13, 'prec': 20, 'unit': 238229652849365033667, 'val': 1}
  • id: 3797270
    {'lmfdb_iso': '73920.gk', 'p': 17, 'prec': 20, 'unit': 60510227831540567356627, 'val': 1}
  • id: 3797267
    {'lmfdb_iso': '73920.gk', 'p': 29, 'prec': 20, 'unit': 341125876161373277500263251, 'val': 1}
  • id: 3797278
    {'lmfdb_iso': '73920.gk', 'p': 31, 'prec': 20, 'unit': 16951158137655470675549286032, 'val': 1}
  • id: 3797263
    {'lmfdb_iso': '73920.gk', 'p': 37, 'prec': 20, 'unit': 401150189466480245166433348905, 'val': 1}
  • id: 3797265
    {'lmfdb_iso': '73920.gk', 'p': 41, 'prec': 20, 'unit': 2825856086956602641924326552147, 'val': 1}
  • id: 3797266
    {'lmfdb_iso': '73920.gk', 'p': 43, 'prec': 20, 'unit': 437337314463081196337832050309, 'val': 1}
  • id: 3797276
    {'lmfdb_iso': '73920.gk', 'p': 47, 'prec': 20, 'unit': 16711198377686465117530118790863, 'val': 1}
  • id: 3797272
    {'lmfdb_iso': '73920.gk', 'p': 53, 'prec': 20, 'unit': 45329993278856853572815261869187, 'val': 1}
  • id: 3797273
    {'lmfdb_iso': '73920.gk', 'p': 59, 'prec': 20, 'unit': 681044710684370274527940172933921, 'val': 1}
  • id: 3797277
    {'lmfdb_iso': '73920.gk', 'p': 61, 'prec': 20, 'unit': 1428393582270319648840213992908535, 'val': 1}
  • id: 3797262
    {'lmfdb_iso': '73920.gk', 'p': 67, 'prec': 20, 'unit': 33384611455671125527922168857816073, 'val': 1}
  • id: 3797264
    {'lmfdb_iso': '73920.gk', 'p': 71, 'prec': 20, 'unit': 54121499365603952922501509253485649, 'val': 1}
  • id: 3797274
    {'lmfdb_iso': '73920.gk', 'p': 73, 'prec': 20, 'unit': 108943751114985049678231458632209688, 'val': 1}
  • id: 3797269
    {'lmfdb_iso': '73920.gk', 'p': 79, 'prec': 20, 'unit': 1107118822648285598276047177562314913, 'val': 1}
  • id: 3797271
    {'lmfdb_iso': '73920.gk', 'p': 83, 'prec': 20, 'unit': 2607035837056303388491335515430951174, 'val': 1}
  • id: 3797275
    {'lmfdb_iso': '73920.gk', 'p': 89, 'prec': 20, 'unit': 3213510669538524969560018789173740939, 'val': 1}
  • id: 3797261
    {'lmfdb_iso': '73920.gk', 'p': 97, 'prec': 20, 'unit': 13264114779152269297736496438916318546, 'val': 1}